Math Chapter Wise

EnglishUP PCS (Pre) 1995

Q261.The asymptotes of the hyperbola xy (x y) 0 are–

Ax 0, y 0 Bx 0, y Cx, y 0 Dx, y

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EnglishUP PCS (Pre) 1996

Q262.If the normals at the points whose vectorial angle are (,,) on the parabola 1 cos r = + θ = + θ = + θ = + θ l meets in a point (,), then:

A2 B2 C2φ = α +β + γ D2

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EnglishUP PCS (Pre) 1996

Q263.The sum of the squares of semi-conjugate diameters of the ellipse 2 2 x y 1, a b is–

A2 2/a b B2 2/a b C2 2/( a b ) DNone of these

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EnglishUP PCS (Pre) 1996

Q264.The hyperbola 2 2 x y 2 and xy 1:

Ado not intersect Bintersect orthogonally Cintersect but not orthogonally DNone of these

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EnglishUP PCS (Pre) 1996

Q265.If PSP' is a focal chord of the conic 1 1 ecos, r then 1 1 SP SP' + + is equal to:

A1/l B2/l Cl/2 DNone of these

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EnglishUP PCS (Pre) 1996

Q266.The locus of the centres of conics, which touch the co-ordinate axes at distances h and k respectively from the origin, is a straight line:

Akx hy Bhx ky Chx ky DNone of these

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EnglishUP PCS (Pre) 1996

Q267.The equation ax + by = 1 represents a:

Acircle Bparabola Cellipse Dhyperbola

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EnglishUP PCS (Pre) 1996

Q268.The equation 2 r = 1 + 2 cos2 2 θ represents:

AA parabola BAn ellipse CA hyperbola DNone of these

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EnglishUP PCS (Pre) 1999

Q269.The asymptote of the curve sinx y = x + x is:

Ay =1 By =1+x Cy =–x Dy =x

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EnglishUP PCS (Pre) 1999

Q270.The polar equation 2 1 θ = cos r 2 represents:

Aa straight line Ba parapobla of latus rectum 2 Ca parabola of latus rectum 4 Da circle of radius

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EnglishUP PCS (Pre) 1999

Q271.The line x cos α+y sin α = p touches the circle x2 +y2 =a2, a2 >1 if p equals:

Ap = 1 Bp = sin α Cp = –a Dp = cos α

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EnglishUP PCS (Pre) 1999

Q272.The equation (x+2y–4)2 –(2x–y+6)2 = 9 represents:

Aa pair of straight lines Ba parabola Can ellipse Da rectangular hyperbola

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EnglishUP PCS (Pre) 1999

Q273.A point lying on the hyperbola 2 2 x y - = 1 a b is:

A(a sin θ, b cos θ) B(a tan θ, b sec θ) C(a sec θ, b tan θ) D(a, b)

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EnglishUP PCS (Pre) 1999

Q274.A conic of eccentricity e represents an ellipse if:

Ae = 1 B0<e<1 Ce > 1 De = 0

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EnglishUP PCS (Pre) 1999

Q275.The vertex of the parabola y2 –8x–4y–4 = 0 is:

A(1, 2) B(–1, 2) C(1, –2) D(–1, –2)

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EnglishUP PCS (Pre) 1999

Q276.The ecentricity of the hyperbola x2 –2x–4y2 = 0 is:

A5/2 B3/2 C1/4 D2

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EnglishUP PCS (Pre) 2000

Q277.The polar equation r = a sec θ represents a:

Astraight line Bcircle Cparabola Drectangular hyperbola

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EnglishUP PCS (Pre) 2000

Q278.If the pedal equation of the curve is p2 = ar, then the value of ρ is equal to:

Ap Bp/a C2p2//a2 D2p3//a2

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EnglishUP PCS (Pre) 2000

Q279.The asymptotes of the curve y4 + x2 y2 + 2xy2 – 4x2 – y + 1 = 0 parallel to the axis of x are:

Ax = ±2 Bx = ±1 Cy = ±2 Dy = ±1

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EnglishUP PCS (Pre) 2000

Q280.The pedal equation of the rectangular hyperbola x2 – y2 = 4 is:

Apr = 4 Bp = 4r Cp = 4r2 Dpr2 = 4

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